Elliptic curve isogeny class with LMFDB label 176400.sa (Cremona label 176400gr)

• Label: 176400.sa
• Number of curves: $4$
• Conductor: $176400$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $0$

Elliptic curves in class 176400.sa

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
176400.sa1	176400gr4	\([0, 0, 0, -6559875, 6466493250]\)	\(16581375\)	\(1882737888192000000\)	\([2]\)	\(4128768\)	\(2.5676\)		\(-28\)
176400.sa2	176400gr3	\([0, 0, 0, -385875, 113447250]\)	\(-3375\)	\(-1882737888192000000\)	\([2]\)	\(2064384\)	\(2.2210\)		\(-7\)
176400.sa3	176400gr2	\([0, 0, 0, -133875, -18852750]\)	\(16581375\)	\(16003008000000\)	\([2]\)	\(589824\)	\(1.5946\)		\(-28\)
176400.sa4	176400gr1	\([0, 0, 0, -7875, -330750]\)	\(-3375\)	\(-16003008000000\)	\([2]\)	\(294912\)	\(1.2480\)	\(\Gamma_0(N)\)-optimal	\(-7\)

Rank

The elliptic curves in class 176400.sa have rank \(0\).

Complex multiplication

Each elliptic curve in class 176400.sa has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 176400.2.a.sa

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.